How to get reference clip to start in middle of timeline?
Texturing a plane with a video/image- For a Background Image see Edit below...

I'm using vers 2.77a here so 2.79 might be a little different. Here goes - 

Select your model first in the 3D window.

At the extreme right are the 'Properties panels'.  The one with a small brown sphere is the "Material properties panel"  Click on that.

Go to the Texture properties next.  That's shown as a tiny coloured checkerboard of 
sorts.  Click on that.

Go down to the "Image" tab and open that.

Down near the bottom is a tick-box called "Auto Refresh".  Make sure that's ticked to 
make the video play.

At the left of that is a pair of slots - "Start &amp; Offset".

Click in the "Start slot and enter the Blender timeline frame-number that you want the video to commence playing from.

The Offset slot points to the frame number within the video-clip itself that it's to treat as it's first frame.  (like pulling a tape or film strip through a player and starting from there)



EDIT 27th April 2019 - re Movie clip as a Background Image -

The same applies in the bkd image's panel.  

Press N to open up the Viewport's properties. Scroll down to the "Background Image" tab and open that.  Click on the image folder icon to open your movie.

In there you'll see the same tick-boxes and entry slots as mentioned above.

You'll notice the "Opacity" slider is set at half by default.  Wind it up to 100% for full opacity.